Q: If ∫x 3 (√ ((1+x 2 )/(1-x 2 )))dx= A √(1-x 4 ) - Bx 2 (√(1-x 4 ) + C sin -1 (x 2 ) + D ,then A+B+C=?

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Q: If &int;x 3 (&radic; ((1+x 2 )/(1-x 2 )))dx= A &radic;(1-x 4 ) - Bx 2 (&radic;(1-x 4 ) + C sin -1 (x 2 ) + D ,then A+B+C=?

Badiuddin askIITians.ismu Expert · Answer

Dear Tapasranjan &int;x 3 (&radic; ((1+x 2 )/(1-x 2 )))dx= A &radic;(1-x 4 ) - Bx 2 (&radic;(1-x 4 ) + C sin -1 (x 2 ) + D differentiate w.r.t x and simplify x 2 +x 4 = x 2 (-2A) + x 4 (4B) +2C -2B compair coefficient of same power of x -2A =1 A =-1/2 4B =1 B=1/4 2C -2B =0 C=B=1/4 now A+B+C =0 Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE & AIEEE preparation. All the best. Regards, Askiitians Experts Badiuddin

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Q: If ∫x 3 (√ ((1+x 2 )/(1-x 2 )))dx= A √(1-x 4 ) - Bx 2 (√(1-x 4 ) + C sin -1 (x 2 ) + D ,then A+B+C=?

Q: If ∫x³(√ ((1+x²)/(1-x²)))dx= A √(1-x⁴) - Bx²(√(1-x⁴) + C sin^-1(x²) + D ,then A+B+C=?

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Q: If ∫x 3 (√ ((1+x 2 )/(1-x 2 )))dx= A √(1-x 4 ) - Bx 2 (√(1-x 4 ) + C sin -1 (x 2 ) + D ,then A+B+C=?

Q: If ∫x3(√ ((1+x2)/(1-x2)))dx= A √(1-x4) - Bx2(√(1-x4) + C sin-1 (x2) + D ,then A+B+C=?

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Q: If ∫x³(√ ((1+x²)/(1-x²)))dx= A √(1-x⁴) - Bx²(√(1-x⁴) + C sin^-1(x²) + D ,then A+B+C=?